Institute of Mathematical Statistics;Institut Henri Poincar�
摘要:
摘要： We consider a family of nonlinear stochastic heat equations of the form \partial_{t}u=\mathcal{L}u+\sigma(u)\dot{W}, where \dot{W} denotes space–time white noise, \mathcal{L} the generator of a symmetric Lévy process on \mathbf{R} , and \sigma is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure u_{0}. Tight a priori bounds on the moments of the solution are also obtained. ¶ In the particular case that \mathcal{L}f=cf'' for some c>0, we prove that if u_{0} is a finite measure of compact support, then the solution is with probability one a bounded function for all times t>0. 出版者： Institut Henri Poincaré 出版日期： 2014-02-01 出處： Annales de l'I.H.P. Probabilités et statistiques, 2014-02, Vol.50 (1), p.136-153 資源來源： Project Euclid Direct 版權： Copyright 2014 Institut Henri Poincaré 識別號： ISSN: 0246-0203 識別號： ISSN: 1778-7017 識別號： DOI: 10.1214/12-AIHP505
